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Simplifying x2 + 63x + 63 = 0 Reorder the terms: 63 + 63x + x2 = 0 Solving 63 + 63x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-63' to each side of the equation. 63 + 63x + -63 + x2 = 0 + -63 Reorder the terms: 63 + -63 + 63x + x2 = 0 + -63 Combine like terms: 63 + -63 = 0 0 + 63x + x2 = 0 + -63 63x + x2 = 0 + -63 Combine like terms: 0 + -63 = -63 63x + x2 = -63 The x term is 63x. Take half its coefficient (31.5). Square it (992.25) and add it to both sides. Add '992.25' to each side of the equation. 63x + 992.25 + x2 = -63 + 992.25 Reorder the terms: 992.25 + 63x + x2 = -63 + 992.25 Combine like terms: -63 + 992.25 = 929.25 992.25 + 63x + x2 = 929.25 Factor a perfect square on the left side: (x + 31.5)(x + 31.5) = 929.25 Calculate the square root of the right side: 30.483602149 Break this problem into two subproblems by setting (x + 31.5) equal to 30.483602149 and -30.483602149.Subproblem 1
x + 31.5 = 30.483602149 Simplifying x + 31.5 = 30.483602149 Reorder the terms: 31.5 + x = 30.483602149 Solving 31.5 + x = 30.483602149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31.5' to each side of the equation. 31.5 + -31.5 + x = 30.483602149 + -31.5 Combine like terms: 31.5 + -31.5 = 0.0 0.0 + x = 30.483602149 + -31.5 x = 30.483602149 + -31.5 Combine like terms: 30.483602149 + -31.5 = -1.016397851 x = -1.016397851 Simplifying x = -1.016397851Subproblem 2
x + 31.5 = -30.483602149 Simplifying x + 31.5 = -30.483602149 Reorder the terms: 31.5 + x = -30.483602149 Solving 31.5 + x = -30.483602149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31.5' to each side of the equation. 31.5 + -31.5 + x = -30.483602149 + -31.5 Combine like terms: 31.5 + -31.5 = 0.0 0.0 + x = -30.483602149 + -31.5 x = -30.483602149 + -31.5 Combine like terms: -30.483602149 + -31.5 = -61.983602149 x = -61.983602149 Simplifying x = -61.983602149Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.016397851, -61.983602149}
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